Optimal control on the mathematical models of dengue epidemic by giving vaccination and repellent strategies

Abstract

Dengue is a very dangerous disease in the tropic and subtropic areas. This disease is transmitted through the bite of an infected female Aedes Aegypti. In this study, optimal control of the dengue model will be discussed by applying 3 strategies, there are vaccination, repellent, and both of them. A dengue epidemic model was built without control with assumptions given by facts obtained by researchers. Then from the model, the equilibrium point is formulated and the equilibrium point stability of the model is evaluated. The next discussion is to determine the optimal control of the dengue epidemic model and minimize the costs of implementing controls. Numerical simulation results showed that 3rd strategy, which is vaccination and repellent, can reduce the subpopulations number of humans infected by dengue with the minimum cost of implementing control.